The standard testing procedures for seasonal unit roots developed so far have been based0501nly on time invariant ARMA processes with AR polynomials involving seasonal differencing. One attractive alternative is to employ periodic ARMA models in which the coefficients are allowed to vary with the season. In this paper, we present convenient procedures for testing for the presence of unit roots at the zero and seasonal frequencies in periodic time series. The limiting distributions of these statistics are derived and tabulated. Simulation evidence illustrates the advantages of allowing for periodicity in this context when it is present. The tests are illustrated via applications to macroeconomic and ozone level data.